The Rieffel deformation of homogeneous spaces
Pawel Kasprzak (University of Copenhagen)
Tuesday 20th April, 2010 16:00-17:00 214
Let H be a closed subgroup of a locally compact group G, and let X be the quotient space of cosets. Also, let L be an abelian closed subgroup of H and f be a 2-cocycle on the dual group of L. Using these data, we can define an action of the quantum group G(f) (the Rieffel deformation of G) on the Rieffel deformation of X. On the other hand, we can perform the Rieffel deformation of the subgroup H obtaining the quantum subgroup H(f) of G(f). This in turn, by the results of Vaes, leads to the C*-algebraic quotient G(f)/H(f). The aim of this talk is to show that two construction described above give isomorphic quantum homogeneous spaces.